Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the
In this study, the modified Rayleigh-Ritz method and Fourier series are used to determine the thermal buckling behavior of laminated composite thin plates with a general elastic boundary condition applied to in-plane uniform temperature distribution depending upon classical laminated plate theory(CLPT). A generalized procedure solution is developed for the Rayleigh-Ritz method combined with the synthetic spring technique. The transverse displacement of the orthotropic rectangular plates is not a different term as a new shape expansion of trigonometric series. In this solution approach, the plate transverse deflection and rotation due to bending are developed into principle Fourier series with a sufficient smoothness auxi
... Show MoreLinear and nonlinear optical properties of epoxy/ Al2O3 nanocomposites system were studied for epoxy neat and (0.5, 1.5, 3, and 5) % Al2O3 nanocomposites.The band gap of epoxy and its nanocomposites was obtained at these weight ratios. Nonlinear optical properties experiments were performed using Q-switched Nd:YAG laser z-scan system.These experiments were carried out for different parameters: wavelengths (1064 nm and 532 nm), laser intensities (0.530, 0.679, and 0.772) GW/cm2 and weight ratio of Al2O3 nanocomposites. The results showed that the band gaps were decreased with increasing the weight ratio of nanoalumina except at 5wt% and the nonlinear refractive index coefficient is directly proportional to the incident intensities while o
... Show MoreThis paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.
Electromechanical actuators are used in a wide variety of aerospace applications such as missiles, aircrafts and spy-fly etc. In this work a linear and nonlinear fin actuator mathematical model has been developed and its response is investigated by developing an algorithm for the system using MATLAB. The algorithm used to the linear model is the state space algorithm while the algorithm used to the nonlinear model is the discrete algorithm. The huge moment constant is varied from (-3000 to 3000) and the damping ratio is varied from (0.4 to 0.8).
The comparison between linear and nonlinear fin actuator response results shows that for linear model, the maximum overshoot is about 10%,
... Show MoreIn this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.
This work intends to illustrate the methods of using the authentic literary text in the process of spreading Italian, especially in Baghdad where there is a strong propensity to learn the Italian language. The concept of the language that arises from literature is an idea closely linked to the mentality of the Arab learner towards Italian culture: an idea also created by the first Arabisations of literary texts in the early years of the previous century. The research was carried out in Baghdad by two researchers, an Italianist from Baghdad and an Italian mother language linguist, with the aim of bringing together the two sectors in favor of the diffusion of the Italian language. The study also aims to clarify the models from Italian l
... Show MoreNonlinear diffraction patterns can be obtained by focusing a laser beam through a thin slice of the material. Here, we investigated experimentally the formation of the far field nonlinear diffraction patterns of cw laser beam at 532 nm passing through a quartz cuvette containing multi-wall carbon nanotubes (MWCNT's) suspended in acetone and in DI water at concentrations of 0.030.wt.%, 0.045 wt.%, 0.060 wt.%, and 0.075 wt.%. Our results show that increasing the concentration of both types of suspensions (MWCNTs in acetone and MWCNTs DI water) led to increase in the number of pattern rings which indicates an increase in their nonlinear refractive indices. Moreover, MWCNTs DI water suspension at a concentration of 0.075 wt. % was more effic
... Show MoreEnergy Loss Function (ELF) of 2 5 Ta O derived from optical limit
and extended to the total part of momentum and their energy
excitation region ELF plays an important function in calculating
energy loss of electron in materials. The parameter Inelastic Mean
Free Path (IMFP) is most important in quantitative surface sensitive
electron spectroscopies, defined as the average distance that an
electron with a given energy travels between successive inelastic
collisions. The stopping cross section and single differential crosssection
SDCS are also calculated and gives good agreement with
previous work.